Solve 24/m+24-m/m-6+m^2+144/m^2+18m-144

$$\frac { 24 } { m + 24 } - \frac { m } { m - 6 } + \frac { m ^ { 2 } + 144 } { m ^ { 2 } + 18 m - 144 }$$

Evaluate

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Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+24 and m-6 is \left(m-6\right)\left(m+24\right). Multiply \frac{24}{m+24} times \frac{m-6}{m-6}. Multiply \frac{m}{m-6} times \frac{m+24}{m+24}.

$$\frac{24\left(m-6\right)}{\left(m-6\right)\left(m+24\right)}-\frac{m\left(m+24\right)}{\left(m-6\right)\left(m+24\right)}+\frac{m^{2}+144}{m^{2}+18m-144}$$

Since \frac{24\left(m-6\right)}{\left(m-6\right)\left(m+24\right)} and \frac{m\left(m+24\right)}{\left(m-6\right)\left(m+24\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24\left(m-6\right)-m\left(m+24\right)}{\left(m-6\right)\left(m+24\right)}+\frac{m^{2}+144}{m^{2}+18m-144}$$

Do the multiplications in 24\left(m-6\right)-m\left(m+24\right).

$$\frac{24m-144-m^{2}-24m}{\left(m-6\right)\left(m+24\right)}+\frac{m^{2}+144}{m^{2}+18m-144}$$

Combine like terms in 24m-144-m^{2}-24m.

$$\frac{-144-m^{2}}{\left(m-6\right)\left(m+24\right)}+\frac{m^{2}+144}{m^{2}+18m-144}$$

Factor m^{2}+18m-144.

$$\frac{-144-m^{2}}{\left(m-6\right)\left(m+24\right)}+\frac{m^{2}+144}{\left(m-6\right)\left(m+24\right)}$$

Since \frac{-144-m^{2}}{\left(m-6\right)\left(m+24\right)} and \frac{m^{2}+144}{\left(m-6\right)\left(m+24\right)} have the same denominator, add them by adding their numerators.

$$\frac{-144-m^{2}+m^{2}+144}{\left(m-6\right)\left(m+24\right)}$$

Combine like terms in -144-m^{2}+m^{2}+144.

$$\frac{0}{\left(m-6\right)\left(m+24\right)}$$

Zero divided by any non-zero term gives zero.

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Factor

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